CN103812587B - A kind of satellite channel modeling method based on group delay effect and nonlinear restriction - Google Patents

Abstract

The invention discloses a kind of modeling method of satellite channel, the non-linear of high power amplifier and group delay nonlinear effect are organically combined, solves the problem of prior art channel model to the simulation tracing degraded performance of real satellite channel.Satellite channel is considered as linear channel, nonlinear channel, group delay channel 1 and group delay channel 2 four part and forms by the present invention innovatively; Each part is gone to approach by the linear segment of Wiener model and non-linear partial respectively, when approximate procedure is restrained, remains Wiener model characteristic; When approximate procedure is not restrained, define a control function substitutes Wiener model nonlinear function as the constraint function of nonlinear channel input and output, to control approximate procedure convergence.Compared with traditional satellite channel Wiener model, invention increases convergence rate, reduce mean square error, there is good performance of dynamic tracking, thus ensure that efficiency and the quality of satellite communication.

Description

A kind of satellite channel modeling method based on group delay effect and nonlinear restriction

Technical field

The invention belongs to technical field of satellite communication, particularly relate to a kind of satellite channel modeling method the non-linear of high power amplifier and group delay nonlinear effect organically combined.

Background technology

In satellite communication, communication quality is relevant with satellite channel characteristic.Whether consistent with actual channel characteristic according to the channel model that satellite channel characteristic is set up, be the key affecting satellite communication quality.And traditional satellite channel model is considered as being formed by the linear channel model of transmitting filter, high power amplifier and the nonlinear channel Cascade of high power amplifier, as shown in Figure 1, conventional model carries out modeling for the non-linearity of high power amplifier, do not consider the impact of uplink communication environment in satellite communication system, emission filter and the group delay effect caused by inside satellite high power amplifier.

Conventional satellite channel model shown in Fig. 1, transmitting filter is Nyquist raised cosine filter, and satellite high power amplifier adopts linearly limits impulse response (FIR) filter and memoryless nonlinear model cascade structure.Wherein, the linear segment of the linear channel model Wiener model of high power amplifier is expressed as

$Y\left(n\right)=\underset{i=0}{\overset{N}{\mathrm{\Σ}}}{W}_1\left(i\right)X(n-i),$

The non-linear of the nonlinear channel model Wiener model of high power amplifier is divided into

$Z\left(n\right)=\underset{j=1}{\overset{M}{\mathrm{\Σ}}}{W}_2(n-j){\left(Y\left(n\right)\right)}^j,$

In formula, W ₁n () represents the linear segment coefficient of Wiener model, W ₂n () represents the non-linear partial coefficient of Wiener model, Y (n) and Z (n) is respectively the output of linear processes part; W ₁(n) and W ₂n () adopts stochastic gradient descent method to upgrade.In the process of approaching to reality satellite channel, there is comparatively big error in this satellite channel Wiener model, even may occur the situation that cannot restrain.Therefore, remove the satellite channel of approaching to reality with the satellite channel Wiener model taking no account of group delay effect, had a strong impact on satellite communication efficiency and quality.

Summary of the invention

For solving the problem, the invention discloses a kind of modeling method of satellite channel, the non-linear of high power amplifier and group delay nonlinear effect are organically combined, solve the problem of prior art channel model to the simulation tracing degraded performance of real satellite channel, effectively improve satellite communication quality.

In order to achieve the above object, the invention provides following technical scheme:

Based on a satellite channel modeling method for group delay effect and nonlinear restriction, comprise the steps:

Steps A, the linear channel of system input signal a (n) obtains its output signal b (n); System input signal a (n) obtains its output signal b through group delay channel 1 ₁(n); System input signal a (n) obtains its output signal b through group delay channel 2 ₂(n); Wherein, n is integer, represents time series;

Step B, outputs signal b (n) by system input signal a (n) described in steps A, linear channel and group delay channel 1 outputs signal b ₁n (), obtains nonlinear channel input signal x (n) through arithmetic unit 1 computing: x (n)=b (n) b ₁(n)/a (n);

Step C, nonlinear channel input signal x (n) described in step B, through nonlinear channel, obtains its output signal y (n);

Step D, system input signal a (n) described in steps A and group delay channel 2 output signal b ₂n () and output signal y of the nonlinear channel described in step C (n), obtain satellite channel final output signal z (n) through arithmetic unit 2 computing: z (n)=y (n) b ₂(n)/a (n);

Described linear channel by emission filter, uplink communication environment and inside satellite high power amplifier without the cascade of group delay linear segment; Nonlinear channel by emission filter, uplink communication environment and inside satellite high power amplifier without the cascade of group delay non-linear partial; Group delay channel 1 represents the nonlinear channel with group delay effect that emission filter, high power amplifier linear segment and uplink communication environment cause; The nonlinear channel with group delay effect that group delay channel 2 represents emission filter, high power amplifier non-linear partial causes;

Wherein, linear channel output b (n) is expressed as by the linear segment of Wiener model:

$b\left(n\right)=\underset{m_0=1}{\overset{M_0}{\mathrm{\Σ}}}{c}_{{0m}_0}\left(n\right)a(n-m_0)$

In formula, m ₀=1 ..., M ₀, M ₀for positive integer; for linear channel C ₀the m of (n) ₀individual time delay tap coefficient; A (n-m ₀) be the n-th-m ₀the signal in moment;

Described group delay channel 1, group delay channel 2 and nonlinear channel are expressed as follows by the non-linear partial of Wiener model:

Wherein, group delay channel 1 is expressed as by the non-linear partial of Wiener model:

$b_1\left(n\right)=\underset{m_1=1}{\overset{M_1}{\mathrm{\Σ}}}{c}_{{1m}_1}\left(n\right){\left(a\left(n\right)\right)}^{m_1}$

In formula, m ₁=1 ..., M ₁, M ₁for positive integer; for group delay channel 1 weight vector C ₁the m of (n) ₁individual time delay tap coefficient;

Group delay channel 2 is expressed as by the non-linear partial of Wiener model:

$b_2\left(n\right)=\underset{m_2=1}{\overset{M_2}{\mathrm{\Σ}}}{c}_{{2m}_2}\left(n\right){\left(a\left(n\right)\right)}^{m_2}$

In formula, m ₂=1 ..., M ₂, M ₂for positive integer; for group delay channel 2 weight vector C ₂the m of (n) ₂individual time delay tap coefficient;

Nonlinear channel AM-AM effect is expressed as by the non-linear partial of Wiener model:

$G\left(n\right)=\underset{m_3=1}{\overset{M_3}{\mathrm{\Σ}}}{c}_{{3m}_3}\left(n\right){\left(\mathrm{\ρ}\left(n\right)\right)}^{M_3};$

In formula, ρ (n)=| x (n) | ²for the amplitude square of nonlinear channel input x (n); m ₃=1 ..., M ₃, M ₃for positive integer; G (n) represents the amplitude of nonlinear channel, for nonlinear channel AM-AM effect weight vector C ₃the m of (n) ₃individual time delay tap coefficient;

Nonlinear channel amplitude modulation-phase modulation effect is expressed as by the non-linear partial of Wiener model:

In formula, represent the phase place of nonlinear channel; m ₄=1 ..., M ₄, M ₄for positive integer; for nonlinear channel amplitude modulation-phase modulation effect weight vector C ₄the m of (n) ₄individual tap coefficient;

Nonlinear channel input x (n)-relation exported between y (n) is expressed as

In formula, for imaginary unit, lower same.

When linear channel is by the linear segment of Wiener model, when group delay channel 1, group delay channel 2 and nonlinear channel represent by the non-linear partial of Wiener model, if this model is not when the process of approaching to reality satellite channel restrains, need retrain the relation between the constrained input of group delay channel 1, group delay channel 2 and nonlinear channel, constraint function is defined as:

$f\left(n\right)=\frac{1-e^{-\mathrm{\α}\left(n\right)}}{1+e^{-\mathrm{\α}\left(n\right)}}$

In formula, α (n) represents input, and f (n) represents output; Represent system input a (n) to group delay channel 1, α (n), f (n) represents the output b of group delay channel 1 ₁(n); Represent system input a (n) to group delay channel 2, α (n), f (n) represents the output b of group delay channel 2 ₂(n); To nonlinear channel, α (n) represents nonlinear channel input x (n), and f (n) represents that nonlinear channel exports y (n);

After using constraint function, nonlinear channel input x (n) is

$x\left(n\right)=\frac{\underset{m_0=0}{\overset{M_0}{\mathrm{\Σ}}}{c}_{{0m}_0}\left(n\right)a(n-m_0)(1-e^{-\underset{m_1=1}{\overset{M_1}{\mathrm{\Σ}}}{c}_{{1m}_1}\left(n\right){\left(a\left(n\right)\right)}^{m_1}})}{a\left(n\right)(1+e^{-\underset{m_1=1}{\overset{M_1}{\mathrm{\Σ}}}{c}_{{1m}_1}\left(n\right){\left(a\left(n\right)\right)}^{m_1}})}$

Satellite channel always exports and is

$z\left(n\right)=\frac{\underset{m_0=0}{\overset{M_0}{\mathrm{\Σ}}}{c}_{{0m}_0}\left(n\right)a(n-m_0)(1-e^{-\underset{m_1=0}{\overset{M_1}{\mathrm{\Σ}}}{c}_{{1m}_1}\left(n\right){\left(a\left(n\right)\right)}^{M_1}})}{a\left(n\right)(1+e^{-\underset{m_1=0}{\overset{M_1}{\mathrm{\Σ}}}{c}_{{1m}_1}\left(n\right){\left(a\left(n\right)\right)}^{M_1}})}\·\frac{(1-e^{-\underset{m_2=0}{\overset{M_2}{\mathrm{\Σ}}}{c}_{{2m}_2}\left(n\right){\left(a\left(n\right)\right)}^{M_2}})}{a\left(n\right)(1+e^{-\underset{m_2=0}{\overset{M_2}{\mathrm{\Σ}}}{c}_{{2m}_2}\left(n\right){\left(a\left(n\right)\right)}^{M_2}})}$

$\·\left(\underset{m_3=1}{\overset{M_3}{\mathrm{\Σ}}}{c}_{{3m}_3}\left(n\right){\left(\mathrm{\ρ}\left(n\right)\right)}^{M_3}\right)e^{j\underset{m_4=1}{\overset{M_4}{\mathrm{\Σ}}}{c}_{{4m}_4}\left(n\right){\left(\mathrm{\ρ}\left(n\right)\right)}^{M_4}}.$

Further,

The weight vector of described linear channel more new formula is:

$C_{{0m}_0}(n+1)=C_{{0m}_0}\left(n\right)+{\mathrm{\λ}}_{0}e\left(n\right)\frac{{\∂e}^{*}\left(n\right)}{{\∂C}_{0m_0}\left(n\right)},$

The weight vector of described group delay channel 1 more new formula is:

$C_{{1m}_1}(n+1)=C_{{1m}_1}\left(n\right)+{\mathrm{\λ}}_{1}e\left(n\right)\frac{{\∂e}^{*}\left(n\right)}{{\∂C}_{1m_1}\left(n\right)},$

The weight vector of described group delay channel 2 more new formula is:

$C_{{2m}_2}(n+1)=C_{{2m}_2}\left(n\right)+{\mathrm{\λ}}_{2}e\left(n\right)\frac{{\∂e}^{*}\left(n\right)}{{\∂C}_{2m_2}\left(n\right)},$

The weight vector of described nonlinear channel AM-AM effect more new formula is:

$C_{{3m}_3}(n+1)=C_{{3m}_3}\left(n\right)+{\mathrm{\λ}}_{3}e\left(n\right)\frac{{\∂e}^{*}\left(n\right)}{{\∂C}_{3m_3}\left(n\right)},$

The weight vector of nonlinear channel amplitude modulation-phase modulation effect more new formula is:

$C_{{4m}_4}(n+1)=C_{{4m}_4}\left(n\right)+{\mathrm{\λ}}_{4}e\left(n\right)\frac{{\∂e}^{*}\left(n\right)}{{\∂C}_{4m_4}\left(n\right)},$

In formula, λ ₀, λ ₁, λ ₂, λ ₃, λ ₄be respectively weight vector and iteration step length, and 0 < λ ₀, λ ₁, λ ₂, λ ₃, λ ₄< 1; $\frac{{\&PartialD;e}^{*}\left(n\right)}{{\&PartialD;C}_{0m_0}\left(n\right)},$ $\frac{{\&PartialD;e}^{*}\left(n\right)}{{\&PartialD;C}_{1m_1}\left(n\right)},$ $\frac{{\&PartialD;e}^{*}\left(n\right)}{{\&PartialD;C}_{2m_2}\left(n\right)},$ $\frac{{\&PartialD;e}^{*}\left(n\right)}{{\&PartialD;C}_{3m_3}\left(n\right)}$ And $\frac{{\&PartialD;e}^{*}\left(n\right)}{{\&PartialD;C}_{4m_4}\left(n\right)}$ Be respectively error function e (n) to weight vector and partial derivative; ^*represent conjugation.

Compared with prior art, tool of the present invention has the following advantages and beneficial effect: satellite channel is considered as linear channel, nonlinear channel, group delay channel 1 and group delay channel 2 four part and forms by the present invention innovatively; Each part is gone to approach by the linear segment of Wiener model and non-linear partial respectively, when approximate procedure is restrained, remains Wiener model characteristic; When approximate procedure is not restrained, define a control function substitutes Wiener model nonlinear function as the constraint function of nonlinear channel input and output, to control approximate procedure convergence.Compared with conventional satellite channel Wiener model, invention increases convergence rate, reduce mean square error, there is good performance of dynamic tracking, thus ensure that efficiency and the quality of satellite communication.

Accompanying drawing explanation

Fig. 1 is satellite channel Wiener model;

Fig. 2 is the satellite channel modeling method schematic diagram based on group delay effect and nonlinear restriction provided by the invention;

Fig. 3 is nonlinear amplifier input power rollback when being 2dB, adopts satellite channel Wiener model and the inventive method to approach the mean square error curve of actual channel respectively;

Fig. 4 is nonlinear amplifier input power rollback when being 4dB, adopts satellite channel Wiener model and the inventive method to approach the mean square error curve of actual channel respectively;

Embodiment

Below with reference to specific embodiment, technical scheme provided by the invention is described in detail, following embodiment should be understood and be only not used in for illustration of the present invention and limit the scope of the invention.

Research shows, the nonlinear effect of high power amplifier is relevant with the instantaneous power of input signal, and group delay effect is relevant with the signal phase nonlinear change that up link satellite communication environment, travelling-wave tube amplifier cause, these two kinds of effects are separate, but the amplitude of signal and phase place have an impact, and then produce AM-AM and amplitude modulation-phase modulation effect.And traditional satellite channel model carries out modeling for the non-linearity of high power amplifier, do not consider the impact of group delay effect.In order to set up the channel model of an approaching to reality satellite channel, on the basis considering the multiple effect of satellite channel, satellite channel is considered as being made up of linear channel, nonlinear channel, group delay channel 1 and group delay channel 2 four parts by the present invention.

Wherein, linear channel by emission filter, uplink communication environment and inside satellite high power amplifier without the cascade of group delay linear segment; Nonlinear channel by emission filter, uplink communication environment and inside satellite high power amplifier without the cascade of group delay non-linear partial, containing AM-AM effect and amplitude modulation-phase modulation effect; Group delay channel 1 represents the nonlinear channel with group delay effect that emission filter, high power amplifier linear segment and uplink communication environment cause; The nonlinear channel with group delay effect that group delay channel 2 represents emission filter, high power amplifier non-linear partial causes.On the satellite channel basis of said structure, the change of tight tracking satellite channel characteristic of the present invention, establishes the satellite channel model with performance of dynamic tracking, and as shown in Figure 2, its step is as follows for schematic diagram:

Steps A, the linear channel of system input signal a (n) obtains its output signal b (n); System input signal a (n) obtains its output signal b through group delay channel 1 ₁(n); System input signal a (n) obtains its output signal b through group delay channel 2 ₂(n):

b(n)＝a(n)C ₀(n) (1)

b ₁(n)＝a(n)C ₁(n) (2)

b ₂(n)＝a(n)C ₂(n) (3)

Wherein, n is integer, represents time series;

Step B, outputs signal b (n) by system input signal a (n) described in steps A, linear channel and group delay channel 1 outputs signal b ₁n (), obtains nonlinear channel input signal x (n) through arithmetic unit 1 computing:

$x\left(n\right)=\frac{b\left(n\right)b_1\left(n\right)}{a\left(n\right)}---\left(4\right)$

Step C, nonlinear channel input signal x (n) described in step B is through nonlinear channel, obtain its output signal y (n), y (n) is for x (n) is by having the nonlinear channel output of AM-AM and amplitude modulation-phase modulation, and contextual definition is therebetween

In formula, G (n) with represent amplitude and the phase place of nonlinear channel respectively; for imaginary unit, lower same.

Step D, system input signal a (n) described in steps A and group delay channel 2 output signal b ₂n () and output signal y of the nonlinear channel described in step C (n), obtain satellite channel final output signal z (n) through internalarithmetic:

$z\left(n\right)=\frac{y\left(n\right)b_2\left(n\right)}{a\left(n\right)}---\left(6\right)$

The present invention C ₀n () represents the weight vector of linear channel; Use C ₁n () represents the weight vector of group delay channel 1; Use C ₂n () represents the weight vector of group delay channel 2; Use C ₃n () represents the weight vector of nonlinear channel AM-AM effect; Use C ₄n () represents the weight vector of nonlinear channel amplitude modulation-phase modulation effect.

Specifically, the weight vector C of linear channel ₀n () is represented by the linear segment of Wiener model, linear channel input a (n)-pass exported between b (n) is

$b\left(n\right)=\underset{m_0=1}{\overset{M_0}{\mathrm{\&Sigma;}}}{c}_{{0m}_0}\left(n\right)a(n-m_0)---\left(7\right)$

In formula, m ₀=1 ..., M ₀, M ₀for positive integer; c _0mn () is linear channel C ₀the m of (n) ₀individual time delay tap coefficient; A (n-m ₀) be the n-th-m ₀the signal in moment;

Group delay channel 1, group delay channel 2 and nonlinear channel are represented by the non-linear partial of Wiener model:

Group delay channel 1 inputs a (n)-output b ₁n the pass between () is

$b_1\left(n\right)=\underset{m_1=1}{\overset{M_1}{\mathrm{\&Sigma;}}}{c}_{{1m}_1}\left(n\right){\left(a\left(n\right)\right)}^{m_1}---\left(8\right)$

In formula, m ₁=1 ..., M ₁, M ₁for positive integer; for group delay channel 1 weight vector C ₁the m of (n) ₁individual time delay tap coefficient; Group delay channel 2 inputs a (n)-output b ₂n the pass between () is

$b_2\left(n\right)=\underset{m_2=1}{\overset{M_2}{\mathrm{\&Sigma;}}}{c}_{{2m}_2}\left(n\right){\left(a\left(n\right)\right)}^{m_2}---\left(9\right)$

In formula, m ₂=1 ..., M ₂, M ₂for positive integer; c _2mn () is group delay channel 2 weight vector C ₂the m of (n) ₂individual time delay tap coefficient; Nonlinear channel AM-AM effect is expressed as by the non-linear partial of Wiener model

$G\left(n\right)=\underset{m_3=1}{\overset{M_3}{\mathrm{\&Sigma;}}}{c}_{{3m}_3}\left(n\right){\left(\mathrm{\&rho;}\left(n\right)\right)}^{M_3}---\left(10\right)$

In formula, ρ (n)=| x (n) | ²for the amplitude square of x (n); m ₃=1 ..., M ₃, M ₃for positive integer; G (n) represents the amplitude of nonlinear channel, for nonlinear channel AM-AM effect weight vector C ₃the m of (n) ₃individual time delay tap coefficient; Nonlinear channel amplitude modulation-phase modulation effect is expressed as by the non-linear partial of Wiener model

In formula, G (n) represents the phase place of nonlinear channel; m ₄=1 ..., M ₄, M ₄for positive integer; for nonlinear channel amplitude modulation-phase modulation effect weight vector C ₄the m of (n) ₄individual time delay tap coefficient.At this moment, nonlinear channel input x (n)-relation exported between y (n) is expressed as

When linear channel is by the linear segment of Wiener model, when group delay channel 1, group delay channel 2 and nonlinear channel represent by the non-linear partial of Wiener model, if this model is not when the process of approaching to reality satellite channel restrains, need retrain the relation between the constrained input of group delay channel 1, group delay channel 2 and nonlinear channel, constraint function is defined as:

$f\left(n\right)=\frac{1-e^{-\mathrm{\&alpha;}\left(n\right)}}{1+e^{-\mathrm{\&alpha;}\left(n\right)}}---\left(13\right)$

In formula, α (n) represents input, and f (n) represents output.

Represent system input a (n) to group delay channel 1, α (n), f (n) represents the output b of group delay channel 1 ₁n (), represent system input a (n) to group delay channel 2, α (n), f (n) represents the output b of group delay channel 2 ₂n (), to nonlinear channel, α (n) represents nonlinear channel input x (n), and f (n) represents that nonlinear channel exports y (n), and after using constraint function, nonlinear channel input x (n) is

$x\left(n\right)=\frac{\underset{m_0=0}{\overset{M_0}{\mathrm{\&Sigma;}}}{c}_{{0m}_0}\left(n\right)a(n-m_0)(1-e^{-\underset{m_1=1}{\overset{M_1}{\mathrm{\&Sigma;}}}{c}_{{1m}_1}\left(n\right){\left(a\left(n\right)\right)}^{m_1}})}{a\left(n\right)(1+e^{-\underset{m_1=1}{\overset{M_1}{\mathrm{\&Sigma;}}}{c}_{{1m}_1}\left(n\right){\left(a\left(n\right)\right)}^{m_1}})}---\left(14\right)$

$z\left(n\right)=\frac{\underset{m_0=0}{\overset{M_0}{\mathrm{\&Sigma;}}}{c}_{{0m}_0}\left(n\right)a(n-m_0)(1-e^{-\underset{m_1=0}{\overset{M_1}{\mathrm{\&Sigma;}}}{c}_{{1m}_1}\left(n\right){\left(a\left(n\right)\right)}^{M_1}})}{a\left(n\right)(1+e^{-\underset{m_1=0}{\overset{M_1}{\mathrm{\&Sigma;}}}{c}_{{1m}_1}\left(n\right){\left(a\left(n\right)\right)}^{M_1}})}\&CenterDot;\frac{(1-e^{-\underset{m_2=0}{\overset{M_2}{\mathrm{\&Sigma;}}}{c}_{{2m}_2}\left(n\right){\left(a\left(n\right)\right)}^{M_2}})}{a\left(n\right)(1+e^{-\underset{m_2=0}{\overset{M_2}{\mathrm{\&Sigma;}}}{c}_{{2m}_2}\left(n\right){\left(a\left(n\right)\right)}^{M_2}})}$

$\&CenterDot;\left(\underset{m_3=1}{\overset{M_3}{\mathrm{\&Sigma;}}}{c}_{{3m}_3}\left(n\right){\left(\mathrm{\&rho;}\left(n\right)\right)}^{M_3}\right)e^{j\underset{m_4=1}{\overset{M_4}{\mathrm{\&Sigma;}}}{c}_{{4m}_4}\left(n\right){\left(\mathrm{\&rho;}\left(n\right)\right)}^{M_4}}---\left(15\right)$

By Fig. 2, error function is defined as

In e (n)=z (n)-d (n) (16) formula, d (n) is the output of real satellite channel.

The cost function of approximate procedure is defined as

J(n)＝E{|e(n)| ²} (17)

In formula, E represents mathematic expectaion.When the cost function of approximate procedure is got minimum, by the descent method of degree of passing at random of cost function, the weight vector obtaining linear channel, group delay channel and nonlinear channel more new formula is

$C_{{0m}_0}(n+1)=C_{{0m}_0}\left(n\right)+{\mathrm{\&lambda;}}_{0}e\left(n\right)\frac{{\&PartialD;e}^{*}\left(n\right)}{{\&PartialD;C}_{0m_0}\left(n\right)}---\left(18\right)$

$C_{{1m}_1}(n+1)=C_{{1m}_1}\left(n\right)+{\mathrm{\&lambda;}}_{1}e\left(n\right)\frac{{\&PartialD;e}^{*}\left(n\right)}{{\&PartialD;C}_{1m_1}\left(n\right)}---\left(19\right)$

$C_{{2m}_2}(n+1)=C_{{2m}_2}\left(n\right)+{\mathrm{\&lambda;}}_{2}e\left(n\right)\frac{{\&PartialD;e}^{*}\left(n\right)}{{\&PartialD;C}_{2m_2}\left(n\right)}---\left(20\right)$

$C_{{3m}_3}(n+1)=C_{{3m}_3}\left(n\right)+{\mathrm{\&lambda;}}_{3}e\left(n\right)\frac{{\&PartialD;e}^{*}\left(n\right)}{{\&PartialD;C}_{3m_3}\left(n\right)}---\left(21\right)$

$C_{{4m}_4}(n+1)=C_{{4m}_4}\left(n\right)+{\mathrm{\&lambda;}}_{4}e\left(n\right)\frac{{\&PartialD;e}^{*}\left(n\right)}{{\&PartialD;C}_{4m_4}\left(n\right)}---\left(22\right)$

In formula, λ ₀, λ ₁, λ ₂, λ ₃, λ ₄be respectively weight vector and iteration step length, and 0 < λ ₀, λ ₁, λ ₂, λ ₃, λ ₄< 1; $\frac{{\&PartialD;e}^{*}\left(n\right)}{{\&PartialD;C}_{0m_0}\left(n\right)},$ $\frac{{\&PartialD;e}^{*}\left(n\right)}{{\&PartialD;C}_{1m_1}\left(n\right)},$ $\frac{{\&PartialD;e}^{*}\left(n\right)}{{\&PartialD;C}_{2m_2}\left(n\right)},$ $\frac{{\&PartialD;e}^{*}\left(n\right)}{{\&PartialD;C}_{3m_3}\left(n\right)}$ And $\frac{{\&PartialD;e}^{*}\left(n\right)}{{\&PartialD;C}_{4m_4}\left(n\right)}$ Be respectively error function e (n) to weight vector and partial derivative; ^*represent conjugation.

Embodiment:

Method provided by the invention and conventional satellite channel Wiener model compare, to verify validity of the present invention further by we.

Experiment adopts transmitting modulation signal to be 8PSK signal, the square root raised cosine filter that transmitting filter is roll-off factor is 0.5, each symbol is 8 sampling points, and weight vector adopts center initialization method; Wiener model neutral line channel and nonlinear channel weight vector iteration step length are 0.0008; In the inventive method, the weight vector number iteration step length of linear channel, nonlinear channel, group delay channel is 0.0005.

Fig. 3 and Fig. 4 is respectively nonlinear amplifier input power rollback when being 2dB and 4dB, and two kinds of methods approach the mean square error curve of actual channel.Input power rollback represents the input signal power of amplifier operation when saturation point and the difference of real input signal power, and its value is less, then non-linear AM-AM and amplitude modulation-phase modulation effect stronger, cause the nonlinear distortion of signal more serious.

Can be found out by Fig. 3 and Fig. 4, at initial period, the mean square error that the inventive method institute established model exports is just little than conventional satellite channel Wiener model.Such as, for input power rollback be 2dB and iteration 1000 times time, the mean square error just 10dB about less of conventional satellite channel Wiener model that the inventive method institute established model exports, and the convergence rate of the inventive method institute established model about 3500 steps faster than conventional satellite channel Wiener model; For input power rollback be 4dB and iteration 1000 times time, the mean square error just 12dB about less of conventional satellite channel Wiener model that the inventive method institute established model exports, and the convergence rate of the inventive method institute established model about 4000 steps faster than conventional satellite channel Wiener model.Therefore, compared with conventional satellite channel Wiener model, the inventive method fast convergence rate, mean square error are little, have good performance of dynamic tracking.

Technological means disclosed in the present invention program is not limited only to the technological means disclosed in above-mentioned execution mode, also comprises the technical scheme be made up of above technical characteristic combination in any.It should be pointed out that for those skilled in the art, under the premise without departing from the principles of the invention, can also make some improvements and modifications, these improvements and modifications are also considered as protection scope of the present invention.

Claims (2)

1., based on a satellite channel modeling method for group delay effect and nonlinear restriction, it is characterized in that, comprise the steps:

Steps A, the linear channel of system input signal a (n) obtains its output signal b (n); System input signal a (n) obtains its output signal b through group delay channel 1 ₁(n); System input signal a (n) obtains its output signal b through group delay channel 2 ₂(n); Wherein, n is integer, represents time series;

Step B, outputs signal b (n) by system input signal a (n) described in steps A, linear channel and group delay channel 1 outputs signal b ₁n (), obtains nonlinear channel input signal x (n) through arithmetic unit 1 computing: x (n)=b (n) b ₁(n)/a (n);

Step C, nonlinear channel input signal x (n) described in step B, through nonlinear channel, obtains its output signal y (n);

Step D, system input signal a (n) described in steps A and group delay channel 2 output signal b ₂n () and output signal y of the nonlinear channel described in step C (n), obtain satellite channel final output signal z (n) through arithmetic unit 2 computing: z (n)=y (n) b ₂(n)/a (n);

Described linear channel by emission filter, uplink communication environment and inside satellite high power amplifier without the cascade of group delay linear segment; Nonlinear channel by emission filter, uplink communication environment and inside satellite high power amplifier without the cascade of group delay non-linear partial; Group delay channel 1 represents the nonlinear channel with group delay effect that emission filter, high power amplifier linear segment and uplink communication environment cause; The nonlinear channel with group delay effect that group delay channel 2 represents emission filter, high power amplifier non-linear partial causes;

Described linear channel is expressed as by the linear segment of Wiener model:

$b\left(n\right)=\underset{m_0=1}{\overset{M_0}{\&Sigma;}}{c}_{0m_0}\left(n\right)a(n-m_0),$

In formula, m ₀=1 ..., M ₀, M ₀for positive integer; for linear channel C ₀the m of (n) ₀individual time delay tap coefficient;

Described group delay channel 1, group delay channel 2 and nonlinear channel are expressed as follows by the non-linear partial of Wiener model:

Wherein, group delay channel 1 is expressed as by the non-linear partial of Wiener model:

$b_1\left(n\right)=\underset{m_1=1}{\overset{M_1}{\&Sigma;}}{c}_{1m_1}\left(n\right){\left(a\right(n\left)\right)}^{m_1},$

In formula, m ₁=1 ..., M ₁, M ₁for positive integer; for group delay channel 1 weight vector C ₁the m of (n) ₁individual time delay tap coefficient;

Group delay channel 2 is expressed as by the non-linear partial of Wiener model:

$b_2\left(n\right)=\underset{m_2=1}{\overset{M_2}{\&Sigma;}}{c}_{2m_2}\left(n\right){\left(a\right(n\left)\right)}^{m_2},$

In formula, m ₂=1 ..., M ₂, M ₂for positive integer; for group delay channel 2 weight vector C ₂the m of (n) ₂individual time delay tap coefficient;

Nonlinear channel AM-AM effect is expressed as by the non-linear partial of Wiener model:

$G\left(n\right)=\underset{m_3=1}{\overset{M_3}{\&Sigma;}}{c}_{3m_3}\left(n\right){\left(\mathrm{\&rho;}\right(n\left)\right)}^{M_3},$

In formula, ρ (n)=| x (n) | ²for the amplitude square of nonlinear channel input x (n); m ₃=1 ..., M ₃, M ₃for positive integer; G (n) represents the amplitude of nonlinear channel, for nonlinear channel AM-AM effect weight vector C ₃the m of (n) ₃individual time delay tap coefficient;

Nonlinear channel amplitude modulation-phase modulation effect is expressed as by the non-linear partial of Wiener model:

In formula, represent the phase place of nonlinear channel; m ₄=1 ..., M ₄, M ₄for positive integer; for nonlinear channel amplitude modulation-phase modulation effect weight vector C ₄the m of (n) ₄individual time delay tap coefficient;

Nonlinear channel input x (n)-relation exported between y (n) is expressed as

In formula, for imaginary unit, lower same;

When linear channel is by the linear segment of Wiener model, when group delay channel 1, group delay channel 2 and nonlinear channel represent by the non-linear partial of Wiener model, if this model is not when the process of approaching to reality satellite channel restrains, need retrain the relation between the constrained input of group delay channel 1, group delay channel 2 and nonlinear channel, constraint function is defined as:

$f\left(n\right)=\frac{1-e^{-\mathrm{\&alpha;}\left(n\right)}}{1+e^{-\mathrm{\&alpha;}\left(n\right)}},$

In formula, α (n) represents input, and f (n) represents output; Represent system input a (n) to group delay channel 1, α (n), f (n) represents the output b of group delay channel 1 ₁(n); Represent system input a (n) to group delay channel 2, α (n), f (n) represents the output b of group delay channel 2 ₂(n); To nonlinear channel, α (n) represents nonlinear channel input x (n), and f (n) represents that nonlinear channel exports y (n);

After using constraint function, nonlinear channel input x (n) is

$x\left(n\right)=\frac{\underset{m_0=0}{\overset{M_0}{\&Sigma;}}{c}_{0m_0}\left(n\right)a(n-m_0)(1-e^{-\underset{m_1=0}{\overset{M_1}{\&Sigma;}}{c}_{1m_1}\left(n\right){\left(a\right(n\left)\right)}^{m_1}})}{a\left(n\right)(1+e^{-\underset{m_1=0}{\overset{M_1}{\&Sigma;}}{c}_{1m_1}\left(n\right){\left(a\right(n\left)\right)}^{m_1}})},$

Satellite channel always exports and is

$\begin{array}{c}z\left(n\right)=\frac{\underset{m_0=0}{\overset{M_0}{\&Sigma;}}{c}_{0m_0}\left(n\right)a(n-m_0)(1-e^{-\underset{m_1=0}{\overset{M_1}{\&Sigma;}}{c}_{1m_1}\left(n\right){\left(a\right(n\left)\right)}^{M_1}})}{a\left(n\right)(1+e^{-\underset{m_1=0}{\overset{M_1}{\&Sigma;}}{c}_{1m_1}\left(n\right){\left(a\right(n\left)\right)}^{M_1}})}\&CenterDot;\frac{(1-e^{-\underset{m_2=0}{\overset{M_2}{\&Sigma;}}{c}_{2m_2}\left(n\right){\left(a\right(n\left)\right)}^{M_2}})}{a\left(n\right)(1+e^{-\underset{m_2=0}{\overset{M_2}{\&Sigma;}}{c}_{2m_2}\left(n\right){\left(a\right(n\left)\right)}^{M_2}})}\\ \&CenterDot;\left(\underset{m_3=0}{\overset{M_3}{\&Sigma;}}{c}_{3m_3}\right(n){\left(\mathrm{\&rho;}\right(n\left)\right)}^{M_3})e^{j\underset{m_4=0}{\overset{M_4}{\&Sigma;}}{c}_{4m_4}\left(n\right){\left(\mathrm{\&rho;}\right(n\left)\right)}^{M_4}}\end{array}.$

2. the satellite channel modeling method based on group delay effect and nonlinear restriction according to claim 1, is characterized in that:

The weight vector of described linear channel more new formula is:

$C_{0m_0}(n+1)=C_{0m_0}\left(n\right)+{\mathrm{\&lambda;}}_{0}e\left(n\right)\frac{\&part;e^{*}\left(n\right)}{\&part;C_{0m_0}\left(n\right)},$

The weight vector of described group delay channel 1 more new formula is:

$C_{1m_1}(n+1)=C_{1m_1}\left(n\right)+{\mathrm{\&lambda;}}_{1}e\left(n\right)\frac{\&part;e^{*}\left(n\right)}{\&part;C_{1m_1}\left(n\right)},$

The weight vector of described group delay channel 2 more new formula is:

$C_{2m_2}(n+1)=C_{2m_2}\left(n\right)+{\mathrm{\&lambda;}}_{2}e\left(n\right)\frac{\&part;e^{*}\left(n\right)}{\&part;C_{2m_2}\left(n\right)},$

The weight vector of described nonlinear channel AM-AM effect more new formula is:

$C_{3m_3}(n+1)=C_{3m_3}\left(n\right)+{\mathrm{\&lambda;}}_{3}e\left(n\right)\frac{\&part;e^{*}\left(n\right)}{\&part;C_{3m_3}\left(n\right)},$

The weight vector of nonlinear channel amplitude modulation-phase modulation effect more new formula is:

$C_{4m_4}(n+1)=C_{4m_4}\left(n\right)+{\mathrm{\&lambda;}}_{4}e\left(n\right)\frac{\&part;e^{*}\left(n\right)}{\&part;C_{4m_4}\left(n\right)},$

In formula, λ ₀, λ ₁, λ ₂, λ ₃, λ ₄be respectively weight vector and iteration step length, and 0 < λ ₀, λ ₁, λ ₂, λ ₃, λ ₄< 1; and be respectively error function e (n) to weight vector and partial derivative; * conjugation is represented.